Question

Raju made 3 different equilateral triangular frames, with side lengths of each are in the ratio 1 : 2 : 3 from
a wire of length 72 cm and Gopi made 3 different square frames whose sides are in the same ratio 1 : 2 : 3
respectively from same length of 72cm wire. Then the ratio of the total area of the figure formed by Raju
and Gopi is :
A) 4 :3 3
B) 4 3 : 7
C) 4 3 :11
D) 4: 7 3
pls answer fast

Answer 1

Solution :-

Let us assume that, side lengths of Equaliteral ∆ are x cm, 2x cm and 3x cm respectively .

so,

→ Total Perimeter of all 3 Equaliteral ∆ = 72 cm .

→ 3 * x + 3 * 2x + 3 * 3x = 72

→ 3(x + 2x + 3x) = 72

→ 3 * 6x = 72

→ 18x = 72

→ x = 4 .

then ,

• side of first Equaliteral ∆ = 4 cm.
• side of second Equaliteral ∆ = 2x = 2 * 4 = 8 cm.
• side of third Equaliteral ∆ = 3x = 3 * 4 = 12 cm.

therefore,

→ Total area of figures formed by raju = (√3/4)[4² + 8² + 12²] = (√3/4) * [16 + 64 + 144] = (√3/4) * 224 = 56√3 cm².

__________

Let us assume that, side lengths of squares are y cm, 2y cm and 3y cm respectively .

so,

→ Total Perimeter of all 3 square = 72 cm .

→ 4 * y + 4 * 2y + 4 * 3y = 72

→ 4(y + 2y + 3y) = 72

→ 4 * 6y = 72

→ 24y = 72

→ y = 3 .

then ,

• side of first square = 3 cm.
• side of second square= 2y = 2 * 3 = 6 cm.
• side of third square = 3y = 3 * 3 = 9 cm.

therefore,

→ Total area of figures formed by Gopi = (3² + 6² + 9²) = 9 + 36 + 81 = 126 cm².

hence,

→ The ratio of the total area of the figure formed by Raju

and Gopi is = 56√3 : 126 = 28√3 : 63 .

Learn more :-

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angle BAC = 111 and AB+BD=AC find the value of angle ACB=?

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